One is to export the flv with audio from AE7. This way you have one file with the video and audio synced.
The second option would be to not use flash video at all. Your animation at this time is pretty simple and could probably be done with bitmaps inside of Flash. This method would use less memory and not suffer compression or buffering issues.
You are right, this one is simple but, most of the time they are not. My problem arises when the client approves the animation but wants change after change to the music. All the re-rendering time in AE just for the music changes would kill me.
Most of my projects develop the same way so unfortunately I can not do suggestion # 1.